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Imaging gate-tunable Tomonaga–Luttinger liquids in 1H-MoSe2 mirror twin boundaries

Abstract

One-dimensional electron systems exhibit fundamentally different properties than higher-dimensional systems. For example, electron–electron interactions in one-dimensional electron systems have been predicted to induce Tomonaga–Luttinger liquid behaviour. Naturally occurring grain boundaries in single-layer transition metal dichalcogenides exhibit one-dimensional conducting channels that have been proposed to host Tomonaga–Luttinger liquids, but charge density wave physics has also been suggested to explain their behaviour. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and tune their charge carrier concentration. Here we present a scanning tunnelling microscopy and spectroscopy study of gate-tunable mirror twin boundaries in single-layer 1H-MoSe2 devices. Gating enables scanning tunnelling microscopy and spectroscopy for different mirror twin boundary electron densities, thus allowing precise characterization of electron–electron interaction effects. Visualization of the resulting mirror twin boundary electronic structure allows unambiguous identification of collective density wave excitations having two velocities, in quantitative agreement with the spin–charge separation predicted by finite-length Tomonaga–Luttinger liquid theory.

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Fig. 1: STM characterization of a SL MoSe2/graphene/hBN/SiO2/Si device at temperature T = 5 K.
Fig. 2: Gate-dependent electronic structure of the MTB.
Fig. 3: Electronic LDOS maps of states at gap edges for Vg = –60 V and Vg = 60 V.
Fig. 4: Experimental (Exp.) STS along MTB at Vg = 0 V compared with theoretical LDOS based on TLL model.
Fig. 5: Gap size statistics and MTB TLL parameter obtained in two different ways.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The codes used in this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

This research was supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences (material growth, STM spectroscopy, theoretical simulations). Support was also provided by the National Science Foundation through grant DMR-1807233 (device design). S.W. and G.Z. acknowledge support by Guangdong Basic and Applied Basic Research Foundation through grant no. 2019A1515110898 (epitaxial graphene growth). Z.Q.Q. acknowledges support by the National Research Foundation of Korea through grant no. 2015M3D1A1070467 (MBE instrumentation development) and no. 2015R1A5A1009962 (MBE growth characterization). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the Ministry of Education, Culture, Sports, Science and Technology, Japan, grant no. JPMXP0112101001 (hBN growth) and the Japan Society for the Promotion of Science KAKENHI grant no. 19H05790 (hBN characterization) and no. JP20H00354 (development of new hBN growth tools).

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T.Z., W.R., F.W. and M.F.C. initiated and conceived this project. W.R., T.Z. and C.Z. carried out STM/STS measurements under the supervision of M.F.C.; Y.-Q.W. and W.R. performed theoretical analysis and numerical calculation under the supervision of J.E.M.; T.Z. and T.W. performed MBE growth under the supervision of Z.Q.Q.; H.-Z.T. and F.L. performed device fabrication under the supervision of M.F.C. and A.Z.; S.W. prepared epitaxial graphene under the supervision of G.Z.; and K.W. and T.T. synthesized hBN crystals. T.Z., W.R., J.B.N., A.W.-B., F.W. and M.F.C. analysed the experimental data. T.Z., W.R., Y.-Q.W. and M.F.C. wrote the manuscript with help from all the authors. All authors contributed to the scientific discussion.

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Correspondence to Wei Ruan, Feng Wang, Joel E. Moore or Michael F. Crommie.

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Zhu, T., Ruan, W., Wang, YQ. et al. Imaging gate-tunable Tomonaga–Luttinger liquids in 1H-MoSe2 mirror twin boundaries. Nat. Mater. 21, 748–753 (2022). https://doi.org/10.1038/s41563-022-01277-3

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